Cart A (m = 2.0 kg) is traveling to the right at 4.0 m/s toward Cart B. Cart Y (m = 8.0 kg) is traveling to the left at 2 m/s. Which cart has the larger magnitude of momentum, and why?

1. Cart Y has a larger magnitude of momentum.

2. Because the mass of cart Y is larger than the mass of cart A.

Explanation:

The following data were obtained from the question:

Mass of cart A (mₐ) = 2 Kg

Velocity of cart A (vₐ) = 4 m/s

Mass of cart Y (mᵧ) = 8 Kg

Velocity of cart Y (vᵧ) = 2 m/s

1. Determination of which of the cart has a larger magnitude of momentum.

For Cart A:

Mass (mₐ) = 2 Kg

Velocity (vₐ) = 4 m/s

Momentum of cart A (pₐ) =?

Momentum = mass × velocity

pₐ = mₐ × vₐ

pₐ = 2 × 4

pₐ = 8 Kgm/s

Thus, the momentum of cart A is 8 Kgm/s

For Cart Y:

Mass (mᵧ) = 8 Kg

Velocity (vᵧ) = 2 m/s

Momentum of cart Y (pᵧ) =?

Momentum = mass × velocity

pᵧ = mᵧ × vᵧ

pᵧ = 8 × 2

pᵧ = 16 Kgm/s

Thus the momentum of cart Y is 16 Kgm/s

SUMMARY:

The momentum of cart A is 8 Kgm/s

The momentum of cart Y is 16 Kgm/s

Therefore, cart Y has a larger magnitude of momentum.

2. Determination of the reason why cart Y has a larger magnitude of momentum.

Momentum is simply defined as the product of mass and velocity i.e

Momentum = mass × velocity

Thus, an increase in either mass or velocity will increase the momentum.

Considering the question given and the solution obtained:

Cart A:

Mass (mₐ) = 2 Kg

Velocity (vₐ) = 4 m/s

Momentum of cart A (pₐ) = 8 Kgm/s

Cart Y:

Mass (mᵧ) = 8 Kg

Velocity (vᵧ) = 2 m/s

Momentum of cart Y (pᵧ) = 16 Kgm/s

From the above data, we can see that the mass of cart Y (i.e 8 Kg) is larger than the mass of cart A (i.e 2 Kg).

Thus, we can conclude that the magnitude of the momentum of cart Y is larger than that of cart A irrespective of their velocities because the mass of cart Y is larger than the mass of cart A.

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